标题： 一个无限维的KAM定理与正常退化 显示英文标题

标题： An Infinite-dimensional KAM Theorem with Normal Degeneracy

摘要： 在本文中，我们考虑一种在法向方向上有退化的经典哈密顿正规形式。 在以前的结果中，需要假设扰动满足某些非退化条件，以便消除正规形式中的退化性。 相反，我们引入了一个拓扑度条件和一个弱凸性条件，这些条件易于验证，并且我们证明了低维环面的存在性，而对扰动没有任何限制，只需其小性和解析性。 显示英文摘要

摘要： In this paper, we consider a classical Hamiltonian normal form with degeneracy in normal direction. In previous results, one needs to assume that the perturbation satisfies certain non-degenerate conditions in order to remove the degeneracy in the normal form. In stead of that, we introduce a topological degree condition and a weak convexity condition, which are easy to be verified, and we prove the persistence of lower dimensional tori without any restriction on perturbation but only smallness and analyticity.